The 17-year-old beat his teenage counterpart to book a second-round meeting with sixth seed Fernando Gonzalez.
The last semi-final spot will be decided on Friday when Gaston Gaudio plays Fernando Gonzalez.
"It will be difficult, but we will do our best for our country, " said player Fernando Gonzalez.
Another shock came when wild card Joachim Johansson saw off the challenge of fourth-seeded Fernando Gonzalez of Chile.
World number eight Fernando Gonzalez of Chile improved his prospects of joining them by booking a place in the quarter-finals.
Federer will play unseeded Nicolas Kiefer in the last four after the German beat fifth seed Fernando Gonzalez 7-6 (7-5) 6-2.
The eight players in the Masters Cup field are: Nadal, Gasquet, Federer, Fernando Gonzalez, Novak Djokovic, Nikolay Davydenko, Andy Roddick and David Ferrer.
The Swiss world number one eventually prevailed 7-6 (7-4) 6-7 (5-7) 6-3 over the Belgian to book a semi-final against Chile's Fernando Gonzalez.
Seventh seed Roddick weathered a storm against Chile's Fernando Gonzalez before winning 6-3 3-6 4-6 7-5 6-2 in a big-hitting contest under the lights.
Murray is back in action on Tuesday and is expecting a much tougher contest against Mathieu, who saw off fifth seed Fernando Gonzalez 6-3 7-6.
There was a shock on Court 13, where seventh seed and Australian Open finalist Fernando Gonzalez of Chile made an early exit to Russia's Teimuraz Gabashvili.
Del Potro, reaching his first U.S. Open semifinals, will face either Fernando Gonzalez or Rafael Nadal, whose quarterfinal match was suspended Thursday night because of rain.
He will next play unseeded Spanish claycourt specialist Juan Carlos Ferrero, who ousted Chilean 10th seed Fernando Gonzalez 4-6 7-5 6-4 4-6 6-4 in an epic clash.
Of his four co-defendants, 49-year-old Fernando Gonzalez, also known as Ruben Campa, is scheduled for release from an Arizona prison Feb. 27, according to the federal Bureau of Prisons.
The remaining quarterfinals take place on Wednesday with top seed Roger Federer facing Chile's Fernando Gonzalez and Spanish fifth seed David Ferrer tackling the sole remaining French hope Gael Monfils.
Chile's Fernando Gonzalez, currently in the eighth and final spot in the race to the World Tour Finals, will play Davydenko in the last 16 after beating Brazilian qualifier Thomaz Bellucci 6-3 6-4.
Cilic will play seventh seed Andy Roddick in the quarterfinals after the American closed out victory over former runner-up Fernando Gonzalez of Chile in their five-setter, which ended in the early hours of the morning.
Fifth seed Robin Soderling of Sweden progressed with a 6-0 6-7 (3-7) 6-2 victory over Chile's Fernando Gonzalez, while Mardy Fish of the U.S. was forced to retire while trailing 6-1 1-0 against 13th seed Mikhail Youzhny.
Djokovic will now face French qualifier Arnaud Clement, a 5-7 6-3 7-6 winner over German 16th seed Tommy Haas, with Del Potro to play Chilean 10th seed Fernando Gonzalez after he beat American John Isner 7-5 7-6.
Andy Murray won the battle of Britain when he beat Tim Henman 6-2 7-6 (7-3), while Fernando Gonzalez of Chile, Carlos Moya of Spain and Tomas Berdych of the Czech Republic also breezed into the round of 16.
Fourteenth seed Tommy Robredo defeated French qualifier Michel Llodra 6-1 6-4, while 10th seed Fernando Gonzalez was handed his place in the next round when Germany's Mischa Zverev retired hurt with a wrist injury in the third set.
The South American duo Juan Martin del Potro and Fernando Gonzalez will both be dangerous opponents, while twice beaten finalist Andy Roddick is being mentioned in dispatches, although the ankle injury he collected at Queen's -- and the suspicion that he isn't quite the player he used to be -- would be a concern.
Real coach Vicente del Bosque will have to decide between Nicolas Anelka and Fernando Morientes to partner Raul Gonzalez in attack.
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